2015年5月4日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2016年5月3日 · Suppose L is a finite dimensional Lie Algebra over an algebraically closed field of characteristic zero. I want to show that $[L,rad(L)]$ is nilpotent. I was given a hint that all operators of the...

Once you know what the set of nilpotent elements is, remember that any quotient of $\mathbb{Z}_{24}$ is a ...

2021年1月17日 · The elements of this set are NOT nilpotent. If you raise this matrix to power, you never will get the zero matrix. Maybe the confusion is because the Lie algebra of this group is the set of nilpotent matrices. $\endgroup$ –

2020年7月18日 · I'm studying nilpotent and solvable group and find it pretty hard to tell what the definition of a nilpotent group is after. For example, a group is solvable iff it has a solvable series (that is, a subnormal series such that each factor is abelian).

2015年3月22日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2019年5月27日 · $\begingroup$ As for your "attempt" and thoughts at the bottom. You say "From my understanding, a nilpotent (matrix) is a matrix such that the eigenvalues of the matrix are all zero.

Subspace of square matrices where all matrices are nilpotent and the products of the matrices are also in the subspace. Hot Network Questions Generate random points from raster layer

2015年7月25日 · And thanks to the commenters (below), I now see that my matrix is indeed nilpotent, since it is upper triangular, with zeros on the main diagonal; in my initial sketch of the matrix - I was way off. :-) (I had thought that the 6's were below the diagonal.) Thanks,

2017年9月4日 · Theorem 9.02. All subgroups and factor groups of the nilpotent group G are nilpotent. If G is of class r then every subgroup and factor group has class r. The definition the author uses for nilpotency class is the following: Definition 1: A group with a central series of length r is said to be nilpotent of class r.